An Efficient Method for the Numerical Solution of Helmholtz-Type General Two-Point Boundary Value Problems in ODEs

In this article, we propose and analyze a computational method for the numerical solution of general two-point boundary value problems in ordinary differential equations (ODEs). The method focuses on Helmholtz-type problems and demonstrates significant improvements in computational efficiency. We have rigorously tested the proposed approach on various benchmark problems to ensure its robustness and accuracy. The results show that our method outperforms existing techniques in the literature, achieving lower maximum absolute errors. This advancement in numerical methodology provides a valuable tool for solving nonlinear and general boundary value problems, offering both stability and precision.